How many solutions are there to the equation

u + v + w + x + y + z = 7

where u, v, w, x, y, and z are nonnegative integers, and x is at most 2 or y is at least 3?

a=listfor(n, 0, 2, (8 - n) nCr 4);print a,"==", sum a==(70, 35, 15) == 120 different solutions

OR:

(8 C 4) + (7 C 4) + (6 C 4)==70 + 35 + 15==120 different solutions

1 - When x is at most 2, there are: 666 solutions

2 - When y is at least 3, there are: 126 solutions.